On orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model

• URL: http://arxiv.org/abs/2606.07449v1
• Date: Fri, 05 Jun 2026 16:51:55 GMT
• Title: On orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model
• Abstract summary: We show that the corresponding transverse linearization is unstable and not stabilizable by linear state feedback.<n>The main contribution is a set of explicit and verifiable conditions that characterize when a controller design based on transverse linearization remains applicable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper addresses orbital stabilization of a circular motion primitive for a dynamic extension of the Dubins car model within a transverse-linearization framework. We show that the corresponding transverse linearization is unstable and not stabilizable by linear state feedback. Therefore, the standard linearization-based approach to orbital stabilization cannot be applied directly. The main contribution is a set of explicit and verifiable conditions that characterize when a controller design based on transverse linearization remains applicable. These conditions rely on the specific structure of the dynamics in a neighborhood of the motion and on the use of non-standard transverse coordinates for controller design and analysis. Numerical simulations illustrate the proposed design procedure.

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